\newcommand{\cosRot}{\begin{pmatrix} 0 \\ 0 \\ \omega \end{pmatrix}}
\newcommand{\der}[1]{\frac{\text{d}#1}{\text{d}t}}
\newcommand{\dder}[1]{\frac{\text{d}^2#1}{\text{d}t^2}}
\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\cphi}{c{\Phi}}
\newcommand{\sphi}{s{\Phi}}
\newcommand{\ctheta}{c{\Theta}}
\newcommand{\stheta}{s{\Theta}}
\newcommand{\cpsi}{c{\Psi}}
\newcommand{\spsi}{s{\Psi}}
\newcommand{\ctrl}[1]{u_{#1}}


\newcommand{\Tibrc}{\ctheta \cdot \cpsi}
\newcommand{\Tibrcc}{\ctheta \cdot \spsi}
\newcommand{\Tibrccc}{- \stheta}
\newcommand{\Tibrrc}{\sphi \cdot \stheta \cdot \cpsi - \cphi \cdot \spsi}
\newcommand{\Tibrrcc}{\sphi \cdot \stheta \cdot \spsi + \cphi \cdot \cpsi }
\newcommand{\Tibrrccc}{ \sphi \cdot \ctheta }
\newcommand{\Tibrrrc}{ \cphi \cdot \stheta \cdot \cpsi +\sphi \cdot \spsi }
\newcommand{\Tibrrrcc}{ \cphi \cdot \stheta \cdot \spsi - \sphi \cdot \cpsi }
\newcommand{\Tibrrrccc}{\cphi \cdot \ctheta}

\newcommand{\Tbirc}{\ctheta \cdot \cpsi}
\newcommand{\Tbircc}{\sphi\cdot \stheta \cdot \cpsi - \cphi \cdot \spsi}
\newcommand{\Tbirccc}{\cphi \cdot \stheta \cdot \cpsi +\sphi \cdot \spsi}
\newcommand{\Tbirrc}{\ctheta \cdot \spsi}
\newcommand{\Tbirrcc}{\sphi \cdot \stheta \cdot \spsi + \cphi \cdot \cpsi }
\newcommand{\Tbirrccc}{\cphi \cdot \stheta \cdot \spsi - \sphi \cdot \cpsi}
\newcommand{\Tbirrrc}{- \stheta}
\newcommand{\Tbirrrcc}{\sphi \cdot \ctheta}
\newcommand{\Tbirrrccc}{\cphi \cdot \ctheta}

\newcommand{\Vbirc}{ 1 }
\newcommand{\Vbircc}{\sphi\cdot t{\theta} }
\newcommand{\Vbirccc}{\cphi \cdot t{\theta}}
\newcommand{\Vbirrc}{ 0 }
\newcommand{\Vbirrcc}{ \cphi }
\newcommand{\Vbirrccc}{ -\sphi }
\newcommand{\Vbirrrc}{ 0 }
\newcommand{\Vbirrrcc}{ \frac{\sphi}{\ctheta} }
\newcommand{\Vbirrrccc}{ \frac{\cphi}{\ctheta} }

\newcommand{\inertia}{\Theta_{body}}
\newcommand{\inertiaii}[1]{\Theta_{b#1}}